00:01
That x represent the amount of money that we win in one game.
00:08
Then we are interested in the probability mass function of x.
00:14
And this will be a piecewise function.
00:17
Well, when we roll that, we get either 1, 2, a 3, a 4, a 5, or a 6.
00:23
For any odd, we get 0.
00:26
For 2 and 4, we get 1.
00:27
For 6, we get 8.
00:29
So that means that there's a 3 in 6 chance, or 1 in 2 chance that x is 0.
00:34
There's a 2 in 6 chance or 1 in 3 chance that x is 1.
00:39
There's a 1 in 6 chance that x is 8.
00:44
For the first question, you got it correctly.
00:47
We're asked to compute the expectation of x.
00:51
And that's just, well, the sum of the product of the probabilities times the values, and you computed it correctly, this will be 5 over 3, or 1 .666666, which rounds up to 1 .667 to 3 decimal places.
01:07
The second question, we need to compute the variance of x...